Fitting a linear model of coregionalization for soil properties using simulated annealing

It is not simple to model cross and auto-variograms to describe the covariation of two or more soil properties, since the models that are fitted must meet certain constraints. These constraints are most readily met by fitting a linear model of coregionalization (LMCR). This presents practical problems. Not all combinations of authorized variogram functions constitute a LMCR. This paper presents a method for automated fitting of variogram functions to auto and cross-variogram estimates, subject to the constraints of the LMCR. The method uses simulated annealing to minimize a weighted sum of squares between the observed and modelled variograms. The method was applied to some data on soil. It was found to be robust to the initial choice of variogram parameters. Practical methods for setting up a good cooling schedule for the simulated annealing are discussed. D 2003 Elsevier Science B.V. All rights reserved.